Problem: Multiply the following complex numbers, marked as blue dots on the graph: $(3 e^{5\pi i / 6}) \cdot (2 e^{3\pi i / 4})$ (Your current answer will be plotted in orange.)
Solution: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $3 e^{5\pi i / 6}$ ) has angle $\frac{5}{6}\pi$ and radius $3$ The second number ( $2 e^{3\pi i / 4}$ ) has angle $\frac{3}{4}\pi$ and radius $2$ The radius of the result will be $3 \cdot 2$ , which is $6$ The angle of the result is $\frac{5}{6}\pi + \frac{3}{4}\pi = \frac{19}{12}\pi$ The radius of the result is $6$ and the angle of the result is $\frac{19}{12}\pi$.